The turmoil hitting the markets and sharp plunge in banking stocks is sparking concern among the euro zone's finance ministers but the president of the group told CNBC that there was no immediate threat of a repeat of the financial crisis.

"Well there is concern (about market volatility), but we also realize we are in a much better situation than we were 10 years ago. Both governments' budgets and the real economy are picking up throughout the euro zone," Eurogroup President Jeroen Dijsselbloem told CNBC on Thursday.

"And our banks are in a much better situation than they were some years ago, a lot of capital has been brought in, balance sheets have been restructured and this process is still continuing with the new rules of the banking union in place," he added.

Jeroen Dijsselbloem

PETRAS MALUKAS | AFP | Getty Images

Global markets have seesawed in the last week on concerns over the performance of global banks amid a low-growth, low interest rate and more regulated environment. On Thursday, European banking equities extended declines, pushing the STOXX 600 European bank index down 6.3 percent by the end of trade.

This week, Credit Suisse stocks have declined 17.6 percent, shares of French banking group Societe Generale has fallen 14.47 percent and Credit Agricole has fallen 11.30 percent. Banking chiefs have told CNBC that the sell-off in banking stocks had been overdone.

The torrid time facing the European banking sector came top of the agenda when the Eurogroup, which comprises the 19-country euro zone's finance ministers, when they met on Thursday in Brussels. But Djisselbloem said that investor concerns reflected wider fears than just the stability of Europe's banks.

"I think a lot of the concerns actually are coming outside of the banking sector, coming from outside the EU, it's about the global economy and emerging markets, it's about the oil price and the impact of that on the real economy. So let's not deviate from the work we are doing which is about strengthening our economy in the euro zone, we're still on that path, and strengthen the banks, which is still ongoing."

He conceded that there were some concerns over the amount of non-performing loans (NPLs) in the European banking sector but that regulatory reforms and new requirements forcing banks to hold a larger amount of capital had made the system safer and more secure.

"I think we all realize, for example, nonperforming loans are an issue in some banks in our country, but over the broad range of our banks a lot of work has been done and a lot of new capital has been brought in and the capital is of a higher standard and quality than some years ago. So we are in a much better position."

Meanwhile, Pierre Moscovici, the commissioner for Economic and Financial Affairs, Taxation and Customs,said the banking sector was "more solid than it used to be" due to the creation of the European banking union, designed to integrate the region's banking sector and strengthen it to help prevent future crises.

"Because we have built the banking union, we know exactly what the situation of the banks is…We are not in the situation that we were in a few years ago," he told CNBC on Thursday.

Moscovici said he didn't want to comment about the psychology of the markets and that the commission was "concerned with this volatility but our message is clear, the fundamentals as well as the real economy and the financial economy of the banking sector are solid enough."

He added that if the sector faced what he called a "delicate situation," Europe had"the means" to address that and said that the stress testing of European banks carried out by the European Central Bank, called the asset quality review, had demonstrated the general strength of the region's banks.

"Overall the asset quality review, the stress tests, show obviously the solidity of the banking sector is much higher than it used to be so, of course, we will be cautious about any kind of risk but we must also keep a cool (head) and face the reality as it is," he said, insisting that the euro zone was not entering another crisis.

"No, we are not in the situation we were in a few years ago. No we are not back there. So we won't be back there because we got all the tools to address any kind of situation now in euro zone."